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Non C-normal operators are dense

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Abstract

A bounded linear operator A acting on a separable complex Hilbert space H is called C-normal with respect to some conjugation C on H if \(CA^*AC=AA^*\). In the present paper, we show that every bounded linear operator A on H can be perturbed by finite-rank operator F with norm as small as desired so that \(A+F\) is not C-normal with respect to any conjugation C.

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Authors and Affiliations

  1. Department of Mathematics, Labo LIABM, Faculty of Science, Mohammed First University, 60000, Oujda, Morocco

    Zouheir Amara & Mourad Oudghiri

Authors
  1. Zouheir Amara
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  2. Mourad Oudghiri
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Correspondence to Zouheir Amara.

Additional information

Communicated by B. V. Rajarama Bhat.

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Amara, Z., Oudghiri, M. Non C-normal operators are dense. Ann. Funct. Anal. 12, 31 (2021). https://doi.org/10.1007/s43034-021-00120-1

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  • DOI: https://doi.org/10.1007/s43034-021-00120-1

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